You can't actually count the number of eggs in an ovary - it doesn't work like this. The eggs are only ripened each cycle from the follicles. You can have scans to determine ovarian reserve which looks at the number of a particular type of follicle visible at any particular moment. As far as I know you can't predict the actual date of menopause from this? You can also not say that once you have been 12 months without a period you will never release another egg. The date is set at 12 months because the majority of women will not ovulate again once thre 12 months time period has elapsed, and to ensure that any woman who bleeds after this point is investigated for potential endometrial hyperplasia which can sometimes lead to cancer. The younger you are the more likely that any bleeding after the 12 months has elapsed is due to spontaneous ovulation.
There are other types of uterine bleeding which can also occur, all of which are abnormal - the most usual of which post-menopause is oestrogen breakthrough bleeding from an over-thickened endometrium. Even after the last ovulation follicles can start to develop but never become a proper egg - any developing follicle produces oestrogen so theoretically the lining can start to thicken a little - hence post-meno bleeding. Women who have fibroids or polyps are also more prone to this.
From what I have read eventually in most women the endometrium atrophies in post-menopause in the absence of HRT and becomes thin, and so doesn't normally bleed.
The short answer is yes you have to wait for 12 months without a bleed before you can say you are post-menopause, but your ovaries may still produce an egg in the future. Pregnancy is extremely unlikely the longer post 45 you get but contraception is still advised for 12 months following last period once you are over 50 and two years if you are under 50.
Hope this helps
Hurdity x